Required Practical: Charging & Discharging Capacitors (AQA A Level Physics): Revision Note

Required practical: charging & discharging capacitors

Aim of the experiment

• The overall aim of this experiment is to calculate the capacitance of a capacitor

• This is just one example of how this required practical might be carried out

Variables

• Independent variable = time, $t$

• Dependent variable = potential difference, $V$

• Control variables:

  • Resistance of the resistor

  • Current in the circuit

Equipment list

• Resolution of measuring equipment:

  • Voltmeter = 0.1 V

  • Stopwatch = 0.01 s

Method

1. Set up the apparatus like the circuit above, making sure the switch is not connected to X or Y (no current should be flowing through).

2. Set the battery pack to a potential difference of 10 V and use a 10 kΩ resistor. The capacitor should initially be fully discharged.

3. Charge the capacitor fully by placing the switch at point X. The voltmeter reading should read the same voltage as the battery (10 V).

4. Move the switch to point Y.

5. Record the voltage reading every 10 s down to a value of 0 V. A total of eight to ten readings should be taken.

• An example table might look like this:

Analysing the results

• The potential difference (p.d) across the capacitance is defined by the equation:

$V=V_0{e}^{-\frac{t}{RC}}$

• Where:

  • $V$ = p.d across the capacitor (V)

  • $V_0$ = initial p.d across the capacitor (V)

  • $e$ = exponential function

  • $t$ = time (s)

  • $R$ = resistance of the resistor (Ω)

  • $C$ = capacitance of the capacitor (F)

• Rearranging this equation for $\ln \left(V\right)$ by taking the natural log ($\ln$) of both sides:

$\ln \left(\frac{V}{V_0}\right)=-\frac{t}{RC}$

$\ln \left(V\right)-\ln \left(V_0\right)=-\frac{t}{RC}$

$\ln \left(V\right)=-\frac{t}{RC}+\ln \left(V_0\right)$

• Comparing this to the equation of a straight line: $y=mx\hspace{0.17em}+c$

  • $y=\ln \left(V\right)$

  • $x=t$

  • $\mathrm{gradient}=-\frac{1}{RC}$

  • $c=\ln \left(V_0\right)$

1. Plot a graph of $\ln \left(V\right)$ against $t$ and draw a line of best fit.

2. Calculate the gradient (this should be negative).

3. The capacitance of the capacitor is equal to:

$C=-\frac{1}{R\times \mathrm{gradient}}$

Evaluating the experiment

• Systematic Errors:

  • If a digital voltmeter is used, wait until the reading is settled on a value if it is switching between two

  • If an analogue voltmeter is used, reduce parallax error by reading the p.d at eye level to the meter

  • Make sure the voltmeter starts at zero to avoid a zero error

• Random Errors:

  • Use a resistor with a large resistance so the capacitor discharges slowly enough for the time to be taken accurately at p.d intervals

  • Using a datalogger will provide more accurate results for the p.d at a certain time

    • This will reduce the error in the speed of the reflex needed to stop the stopwatch at a certain p.d

  • The experiment could be repeated by measuring the time for the capacitor to charge instead

Safety considerations

• Keep water or any fluids away from the electrical equipment

• Make sure no wires or connections are damaged and contain appropriate fuses to avoid a short circuit or a fire

• Using a resistor with too low a resistance will not only mean the capacitor discharges too quickly but also that the wires will become very hot due to the high current

• Capacitors can still retain charge after power is removed which could cause an electric shock

  • These should be fully discharged and removed after a few minutes